Resistance to anti-estrogen therapy is an unsolved clinical challenge in successfully treating ER+ breast cancer patients. Acquisition of mutations can confer heritable resistance to cancer cells, enabling their clonal selection to establish a drug-resistant population. Recent studies have demonstrated that cells can tolerate drug treatment without any genetic alterations too; however, the mechanisms and dynamics of such non-genetic adaptation remain elusive. Here, we investigate coupled dynamics of epithelial-mesenchymal transition (EMT) in breast cancer cells and emergence of reversible drug resistance. Our mechanism-based model for the underlying regulatory network reveals that these two axes can drive one another, thus conferring bidirectional plasticity. This network can also enable non-genetic heterogeneity in a population of cells by allowing for six co-existing phenotypes: epithelial-sensitive, mesenchymal-resistant, hybrid E/M-sensitive, hybrid E/M-resistant, mesenchymal-sensitive and epithelial-resistant, with the first two ones being most dominant. Next, in a population dynamics framework, we exemplify the implications of phenotypic plasticity (both drug-induced and intrinsic stochastic switching) and/or non-genetic heterogeneity in promoting population survival in a mixture of sensitive and resistant cells, even in the absence of any cell-cell cooperation. Finally, we propose the potential therapeutic use of MET (mesenchymal-epithelial transition) inducers besides canonical anti-estrogen therapy to limit the emergence of reversible drug resistance. Our results offer mechanistic insights into empirical observations on EMT and drug resistance and illustrate how such dynamical insights can be exploited for better therapeutic designs.